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Evidence for Tyndall melt-figure production during spallation-induced pressure spikes associated with ice crushing
Cold Regions Science and Technology 167 (2019) 102867
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Evidence for Tyndall melt-figure production during spallation-induced pressure spikes associated with ice crushing
T
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R.E. Gagnona, , C.A. Tulkb a b
Ocean, Coastal and River Engineering, National Research Council Canada, St. John's, NL, Canada Neutron Sciences Directorate, Oak Ridge National Laboratory, Oak Ridge, TN, USA
A R T I C LE I N FO
A B S T R A C T
Keywords: Ice crushing Melt figures Ice/melt slurry layer Pressure spikes Hard-zone erosion
In discussing ice crushing in the brittle regime Gagnon (2016) had speculated that small Tyndall melt figures, functioning in conjunction with a previously observed thin squeeze-film slurry layer of melt and ice particles at the ice/structure interface, could play a role in the removal of ice from the interface. Here we present supporting evidence for the existence of the melt figures. Using high-speed imaging, small features were observed to rapidly appear and grow in size at the ice/surface interface during pressure spikes caused by spallation of ice in the contact zone during crushing experiments conducted at −10 °C. The observations correlate with data from a previous study of inwardly-propagating Tyndall melt figures that nucleate at the surface of ice, situated in an oilfilled pressure vessel, when subjected to rapid adiabatic pressure increments. That is, during the ice-crushing experiments the mean growth length of the features was 1.5 ± 0.6 mm, where associated ice/surface interfacial pressure spikes (from similar tests) were about 36 MPa. For comparison, the earlier melt-figure study yielded a growth length of ~ 1.7 mm, which is within reasonable agreement with the ice-crushing value for the same rapid pressure increment. Furthermore, the features had orientations that generally were aligned with the two diagonal axes that connected opposing corners of the four-sided pyramid-shaped samples, where confinement was greatest. Hence the internal stress, and associated superheating, in hard-zone ice at the crushing interface during pressure spikes was greatest along the two axes. The features tended to grow in these directions, where the most heat was available, so this suggests they were melt figures. An incidence where a twin pair of features exhibited an angular separation close to a crystal symmetry angle also suggests the features were melt figures. The orientation data generally indicate that orientations of melt figures in non-uniformly rapidly-stressed ice may differ from orientations in uniformly stressed ice. We conjecture that in the present study small melt figures form a tenuous liquid matrix of shallow depth (roughly 0.2 mm) in the hard-zone ice surface during pressure spikes. A unique erosive effect may occur as the material in the top portion of this weakened layer is sheared off by, and entrained in, the ambient viscous flow of slurry.
1. Ice crushing characteristics Various aspects of ice crushing in the brittle regime, noted by Gagnon (2016), are illustrated in Fig. 1. The drawing at the left shows an ice shape crushing against a flat platen at a nominal constant rate. In the central region of the contact zone we note a hard zone, where the ice is relatively intact, that causes high interface pressure (~20–70 MPa) at the platen-ice contact region. At the sides of the hard zone is softer crushed ice that essentially is shattered spall debris from prior spalling events. The interface pressure is relatively low (~0–10 MPa) where the crushed ice contacts the platen. At the interface between the hard-zone ice and the platen one can see the thin slurry layer. Note that the slurry is partially liquid and when the slurry layer ⁎
flows out of the hard-zone region it tends to contribute to the wetness of the surrounding crushed ice in the soft zone. Also note that the soft zone itself generates some liquid, due to the same crushing processes, at iceice contact between ice fragments during the extrusion and flow of the crushed ice away from the high-pressure zones (Gagnon, 2013). At the right of the figure we have a schematic showing a spalling fracture just prior to the spall shattering and converting to crushed ice. Here we note that when such a spall forms and shatters there will be a consequent drop in global load and a subsequent increase in stress on the remaining hard-zone ice that causes a sharp spike in interface pressure. Elastic energy in the ice/apparatus system rapidly reduces when the ice and platen surge towards one another as ice is removed from the hard zone due to the flow of the squeeze-film slurry layer during the load drop.
Corresponding author. E-mail address: [email protected] (R.E. Gagnon).
https://doi.org/10.1016/j.coldregions.2019.102867 Received 10 December 2018; Received in revised form 2 May 2019; Accepted 15 August 2019 Available online 16 August 2019 0165-232X/ Crown Copyright © 2019 Published by Elsevier B.V. All rights reserved.
Cold Regions Science and Technology 167 (2019) 102867
R.E. Gagnon and C.A. Tulk
Fig. 1. Schematics showing the essential characteristics of ice crushing against a flat rigid surface. The scenario depicted in the right schematic occurs after the scenario depicted at the left (more details are given below). To highlight the hard zone only a portion of the ice contact zone is shown, that is, the crushed ice at the sides extends farther than what is shown.
2. Experimental and analytical results
Even though the ice may be moving at a nominal constant rate during a crushing test there will nevertheless be compliances associated with the ice, platen and drive system so that the actual relative movement of the ice and platen towards each other is intermittent (Gagnon, 1994a). The removal of ice from the hard-zone surface cannot be fully explained by the melting that occurs due to heat generated by the viscous flow of the slurry since only roughly 20% of the slurry is melt (Gagnon, 1994b).
Fig. 2 shows data from a crushing test on a large single-crystal ice sample (Gagnon, 1994a), where the c-axis was in the loading direction and the test temperature was −10 °C. The mono-crystalline sample ensured good visibility, through the ice specimen, of details of the ice crushing behaviour at the ice-platen contact interface since there were no obscuring intergranular cracks. In this case there are pressure data from a small pressure transducer that was located at the ice-platen interface at the approximate hard-zone location. Furthermore, the figure
Fig. 2. Sections of the load, pressure and liquid-sensor data from a crushing test on a large single-crystal ice sample. From Gagnon, 1994a. 2
Cold Regions Science and Technology 167 (2019) 102867
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shows data from a small (resistance-type) liquid sensor that was located on the face of the pressure transducer. The course phase relationships of data in Fig. 2 have been discussed before (Gagnon, 1994a). Fig. 2 indicates that the associated peaks in load, pressure and liquid thickness occur at roughly the same time. Closer inspection of seven of the prominent load-drop events revealed that the pressure-spike peak typically occurred at ~0.8 ± 0.2 ms after the load peak, and the peak in liquid thickness occurred at ~1.2 ± 0.2 ms after the load peak. Hence, the sequence involves first the spall formation (i.e. initiation of the sharp drop in global load); followed by the increase in stress on the remaining ice (i.e. the pressure spike); followed by the spike in liquid thickness that occurs at the time corresponding to roughly the midpoint of the drop in load (~1.4 ± 0.1 ms after the load peak), where the ice and platen are moving the fastest towards one another and squeezing the viscous slurry out of the contact zone at the fastest rate, thereby creating melt at the fastest rate. The sequence of events, including calculations of the amount of melting and the layer thickness, are discussed by Gagnon (1994a, 2016). Note that the calculations (Gagnon, 1994a) are based on squeeze-film theory that explains why the layer is thinner on the ascending portions of the load peak and at the bottom of the load drop, where the relative speed of the ice moving towards the platen is low. At the midpoint of the load drop the relative speed is much higher and the theory consequently indicates a thicker layer, as is consistent with Fig. 2. The calculations were based on the nominal displacement of the test actuator, the measured load and known compliances of the ice/apparatus system, and the measured hard-zone contact areas. Here we briefly describe what melt figures (a.k.a. negative crystals, in the context of mineralogy) are. If ice near its melting temperature is rapidly pressurized, such as inside a fluid-filled pressure vessel, its melting temperature rapidly decreases, as stipulated by the well-known Clausius-Clapeyron equation (Hobbs, 1974; Baumann et al., 1984). This puts the bulk ice into a superheated state so that the excess heat causes the growth of liquid-filled, sometimes faceted, structures inside the ice. Gagnon et al. (1994) described dendritic fern-like melt figures that nucleated at the ice surface of mono-crystalline samples and grew inwards at a rate proportional to the rate of pressure application (Fig. 3, and the included AVI file ‘Melt_Figure_Growth.avi’). Relieving the pressure reversed the growth process and caused the figures to shrink at a rate proportional to the rate of decompression. Advancing dendrites were very thin (~20 μm). In contrast to the dendritic figures, diskshaped, liquid-filled compression melt fractures were also created by the adiabatic pressurization. These nucleated within the crystal matrix when a certain degree of superheating had been reached. Pressure vessels have been used extensively to study ice mechanics in the context of ice engineering and glaciology, as illustrated in the survey by Barrette (2001). Fundamental studies of nucleation and growth of ice crystals and melt figures, and structural and acoustic properties of high-pressure ice polymorphs, have also been conducted using pressure vessels (e.g. Kaiser and Magun, 1964; Baumann et al., 1984; Gagnon et al., 1990; Kirby et al., 1985), including diamond anvil cells (e.g. Lee et al., 2007; Boehler et al., 2013). Note that other than the study of Gagnon et al. (1994), no other data are available on melt-figure growth rate as a function of pressurization rate. During recent re-analysis of high-speed imaging (30,000 images/s) records from ice crushing experiments (Gagnon, 2008), it was observed that small faint features appeared at the hard zone/platen interface that had characteristics reminiscent of the melt figures observed by Gagnon et al. (1994). The ice samples were large single-crystals where the c-axis was in the loading direction. The ice crushing experiments were set up for relatively large-scale viewing of the ice-crushing behavior where the field of view of the ice/platen interface was around 43 mm, whereas the field of view for the melt-figure study was about 2.2 mm. Additionally, the lighting was different in the two cases, i.e. the lighting was optimized for observing melt figures in the earlier study and not so for the ice crushing study. Nevertheless, it was possible to identify and catalog
Fig. 3. Growth of a dendritic melt figure parallel to the ice crystal basal plane as pressure was elevated during one stroke of the hand pump. The increment in time between consecutive images was 1/15 s. The pressurization rate was 623 bars/s. The diameter of the circular aperture is ~2.2 mm. The ambient temperature was −5 °C. From Gagnon et al., 1994.
several (21) small faint elongated features that appeared within the hard-zone surface interface during pressure spikes. Fig. 4 shows some examples. Common characteristics of the features were: (1) They occurred during pressure spikes associated with spalling events; (2) They rapidly appeared (within one image interval) on the increasing side of the pressure spike and retracted during the latter part of the spike. For example, Fig. 5 (and the included AVI file ‘Faint_Object_Growth_and_Retraction.avi’) shows images illustrating the growth and retraction of a feature. (3) A significant observation (discussed later) is that there were two fairly distinct orientations that the features had in the plane of view. Of the nineteen features that were suitable to use for angular measurements, thirteen of the them leaned towards the right at an angle of 44 ± 13° from the vertical axis and six of the features leaned towards the left at an angle of 47 ± 17°, that is, the angular separation between the two groups was 91 ± 21°. (4) It seemed that they grew in the direction where the most excess heat was 3
Cold Regions Science and Technology 167 (2019) 102867
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Fig. 4. Some examples of the small features (inside the outlined areas) from an ice crushing experiment (Gagnon, 2008) that had characteristics similar to melt figures observed by Gagnon et al. (1994). The images are enhanced to make the small features more visible. The variable-shaped dark areas of the images correspond to relatively-intact hard-zone ice, where the interface contact pressure with the transparent crushing platen is high. The white areas encompassing the dark regions generally correspond to low interface-pressure soft-zone crushed ice. The width of each image box is ~12.6 mm.
available from the pressure-induced super-heating effect. For example, they grew away from any nearby spalling event. (5) They grew mainly laterally within a thin layer of ice at the surface of the hard-zone interface. This common characteristic is explained in the following paragraph. The evidence that the faint features grew laterally within a thin top layer of the hard zones is as follows: 1. The confining geometry of the sloped sides of the bulk ice shape and the even gentler sloped sides of the intact-ice process surface throughout the crushing event implied that the pressure, and degree of ice compression and superheating, was maximal at the interface and dropped off significantly with depth away from the interface. By definition, melt figures grow into regions where the most excess heat, from pressure-induced superheating, is available for melting. That implies that if the faint features were in fact melt figures then they would tend to grow in directions close to the interface, i.e. laterally within a thin top ice layer. 2. If there was a tendency for the faint features to grow in non-lateral directions, for example in directions closer to the normal to the interface, then the distribution of maximal feature lengths (from the perspective of the camera viewing in the normal direction) shown in Fig. 6 would be significantly populated throughout the range from 0 mm to the higher values. However, the data in the figure indicates an average length value of 1.5 mm with a relatively tight standard deviation of ± 0.6 mm, that is, very few data points are less than 1 mm, implying that the faint features do indeed grow in directions close to the interface. In consideration of point 1 above, this suggests that they were melt figures. 3. From the analysis below, for a typical pressure spike of 36.0 MPa there is good agreement between the average apparent maximal length of the faint features in the crushing tests (1.5 ± 0.6 mm) and the growth length of melt figures from the earlier study (1.7 mm). And we know from point 2 above that the growth of the faint features is only in lateral directions. These two facts are mutually consistent if we allow that the faint features are melt figures.
Fig. 5. A numbered set of sequential images of a typical small faint feature (inside the circle) from an ice crushing experiment (Gagnon, 2008). The growth and retraction characteristics of the feature are similar to those of melt figures observed by Gagnon et al. (1994). The images were captured at 30,000 images/ s and are enhanced to make the small feature more visible. The dark area of the images corresponds to relatively-intact hard-zone ice, where the interface contact pressure with the transparent crushing platen is high. The white area encompassing the dark region corresponds to low interface-pressure soft-zone crushed ice. The width of each image box is ~12.6 mm.
Fig. 6. Maximal feature length versus measurement number for the 21 small faint features that were cataloged from the ice crushing experiment. Measurement numbers are indexes that started at a certain time in the visual record, with the first measurement, and progressed forward in time through the record to the last measurement. The ice-crushing experiment was reported by Gagnon (2008). The test was run at −10 °C with a nominal actuator speed of 3.2 cm/s. Length measurements, obtained from the high-speed images, were accurate to within 1 pixel (~0.2 mm). 4
Cold Regions Science and Technology 167 (2019) 102867
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Our intention in this study is to demonstrate that the features observed during the crushing experiments have the same characteristics as melt figures observed during rapid adiabatic pressurization of ice. One means of providing convincing evidence for this will rely on having a good estimate for the actual pressure-spike value associated with a typical spalling event, that is, where the hard zone size and shape, and the spall characteristics, with respect to the pressure-sensor particulars have been reasonably accounted for. We now describe the strategy used to estimate what the actual value of pressure spikes are during spalling events. To do this we first note that the highest non-spike pressure recorded was approximately 60 MPa, as seen in a few tests using the same apparatus and ice type. Since the hard zones were typically a few square centimeters in area, it is reasonable to assume that this maximal nonspike pressure corresponds to those occasional instances where the shape, location and size of the hard zone caused it to fully encompass the circular end of the cylindrical pressure sensor that has a surface area of 0.5 cm2. This implies that for a typical pressure sawtooth we can estimate the fractional areal coverage of the pressure sensor by hardzone ice by taking the measured pressure on the sensor at the base of the pressure spike and assuming that a portion of the surface area of the sensor is covered by hard-zone ice (where the pressure is 60 MPa) and the remainder is covered by soft-zone ice (where the pressure is 5 MPa). This yields a unique value for the fractional hard-zone coverage. For any given pressure range, if we choose the largest pressure spikes in that pressure region we will have some assurance that the hard-zone area under the sensor is not encompassed to any significant extent by the spall that forms. Furthermore, we must choose a particular type of pressure spike, that is, spikes where the pressure just prior to the spike is similar to the value that it is just after the spike, implying that the spallation that caused the spike most likely occurred outside of the area of the pressure sensor. Hence, by choosing the spikes with the highest magnitude (6.5–18.5 MPa) that fit the latter criteria we achieve the greatest likelihood of obtaining a good actual spike-height estimate. In other words, for the chosen pressure spikes the amounts of hard-zone ice contact and soft-zone ice contact under the pressure sensor face have not changed during the ascending portion of the pressure spike, during which no relative movement of the ice and sensor towards each other occurs. Recall that the rapid surge of the ice and crushing platen towards one another starts during the descending part of the pressure spike and is greatest at the midpoint of the drop in load. Note that the crushed-ice soft zone does not contribute anything to the pressure spikes. Generally there are many instances in the lowerpressure data from the pressure sensor, where low pressure indicates that only soft-zone ice is in contact with the sensor. In those cases no spike is registered by the sensor when a spallation occurs.
Fig. 8. Data acquired by analyzing a set of pressure spikes from the same ice crushing experiment corresponding to Fig. 7. The data points (red squares) with fractional coverage greater than 0.25 demonstrate consistency, and therefore yield a reasonable estimate for a typical pressure spike height (36.0 ± 2.4 MPa). The data points (blue diamonds) with fractional coverage less than 0.25 lack consistency, for reasons discussed in the text, and consequently cannot be used to estimate a typical pressure spike height. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
As an example of the strategy, consider the suitably-chosen spike shown in Fig. 7 where we note that the pressure just before the spike is about 33.3 MPa, which implies a coverage of 52% from the hard-zone coverage estimate. Hence, the magnitude of the measured pressure spike (18.5 MPa) is actually only 52% of the true pressure spike on the hard-zone ice since only 52% of the sensor is covered by the hard-zone ice. Therefore we can estimate a true value for a typical pressure spike by multiplying the value of the measured spike by 1/0.52, to yield 35.6 MPa. This would be the measured pressure spike magnitude if the sensor had been fully encompassed by the hard zone and if the spallation occurred outside the pressure sensor area. We have performed this type of analysis for several suitably-chosen pressure spikes in the load record and plotted the estimated actual pressure-spike height in each case in Fig. 8. We note that for data points associated with fractional coverages higher than 0.25 that there is good consistency, where the mean value and standard deviation for these data are 36.0 ± 2.4 MPa. The likely reason why the data points at the left of the plot in Fig. 8, for fractional area coverages less than 0.25, lead to overestimates of spike values (that should not be used) is that at the lower sensor loads the assumption that the sensor is fully covered by only soft ice, or portions of soft ice and hard ice, is probably false. That is, at low
Fig. 7. Graph illustrating the strategy used to analyze pressure spikes. This particular ice crushing experiment was reported by Gagnon (1994b). The test was conducted at −10 °C with a nominal actuator speed of 1.5 cm/s. 5
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This pressure spike would cause a melt figure to grow to a length of 1.7 mm, which agrees quite well with the average length of the features observed in the ice crushing study (1.5 mm), considering the radically different nature of the two studies. The data shown in Figs. 9 and 10 essentially indicate that at these adiabatic pressurization rates (~104 MPa/s and ~68 MPa/s) the rate does not play a role in the growth length of the figures, rather it is the magnitude of the pressure increment that determines the melt-figure growth length (i.e. 0.0472 mm/MPa). We have assumed that this applies even when pressurization rates are as high as those associated with the pressure spikes in the crushing tests (~ 37 GPa/s). The agreement of the melt-figure lengths from the pressure vessel tests and the feature lengths, if we allow that they are melt figures, from the crushing test is consistent with this assumption. We now draw the reader's attention back to the important earlier observation that the features generally had two typical orientations (with some degree of variability) in the plane of view, where the angular separation between the orientations was 91 ± 21°. In a single incidence a twin pair of the features started growth at the same time and from the same location (see the image at the lower right of Fig. 4), where the angular separation between them (~ 116°) was quite close to the crystal symmetry angle of 120°. Gagnon et al. (1994) observed meltfigure growth in the basal plane with orientations that reflected the crystal symmetries (0°, 60°, 120°) and also melt figures with two orientations in a plane perpendicular to the basal plane where the angular separation was 90°. The similarity of the latter with the general angular separations we observed for the features, and the similarity of the angle between the twin pair of features with the symmetry angle of 120°, suggested a connection with the crystal structure though it was not clear why the feature orientations didn't generally reflect the basal plane symmetries (i.e. 0°, 60°, 120°). We offer that these observations may be understood by considering the different ice stress regimes in the two cases. The pressure vessel experiments of Gagnon et al. (1994) involved subjecting the small mono-crystalline ice samples to a uniform hydrostatic stress whereas here we are discussing relatively large monocrystalline pyramid-shaped ice samples that are loaded uniaxially from the top of the pyramid, thereby creating a non-uniform stress field in the ice sample. Allowing that the features are melt figures, the implication is that non-uniform stress fields in ice can alter/perturb the orientations that adiabatic pressure-induced melt figures would normally have in uniformly-stressed ice where the crystalline structure (that reflects variations in the molecular energy levels in the lattice) is the determining factor for melt-figure growth directions. In that connection recall that the two typical orientations of the features (i.e. 44 ± 13° to the right of the vertical axis and to the left of the axis at 47 ± 17°) closely aligned with the diagonals connecting opposing corners of the four-sided pyramid-shaped ice sample. Hence, during loading of the sample confinement was greatest at the corners, implying that internal stress and associated superheating in hard-zone ice at the crushing interface during pressure spikes was greatest along the diagonals. This implies that the features were melt figures, since they tended to grow in directions where the most heat was available. The twin pair of features (Fig. 4, lower right), mentioned above, may have been a special case. Allowing that they are melt figures, we suggest that since the twin pair originated simultaneously from the same location their angular separation (that falls within the general angular variability of singular features) was more inclined to reflect the actual crystal symmetry, as observed. This also provides evidence that the features were melt figures. The influence that ice sample shape has on confinement aspects of the bulk ice is manifested in the typical shapes of hard zones that consequently develop during crushing. For example, Gagnon (1998) observed X-shaped hard zones during crushing tests on large four-sided truncated pyramid-shaped ice features. The ‘arms’ of the ‘X’ aligned with the corners of the pyramids, where confinement was greatest. Spencer and Masterson (1993) have discussed aspect-ratio
Fig. 9. Melt figure growth length versus time for two melt figures. The growth rates (i.e. the slopes of the fitted lines) are different because the pressurization rates were different.
pressures (i.e. small sensor-face loads) a portion of the sensor face may not be in contact with any ice, whether soft or hard. Our assumption would then lead us to overestimate the soft-zone coverage and thereby underestimate the hard-zone ice coverage. This, in turn, would lead us to overcompensate for the assumed small size of the hard-zone coverage on the sensor face when calculating the actual hard-zone pressure. The trend-slope of the first four points at the left of Fig. 8 supports this assertion since the error, caused by no ice contact on a portion of the sensor face, becomes more likely as the load on its face (i.e. the average pressure) gets smaller. From these considerations we may determine the growth length of a melt figure from the study of melt figures (Gagnon et al., 1994) that corresponds with a typical pressure spike (36.0 MPa) from the icecrushing study of Gagnon (1994b). To do this we first use video and pressure records from the melt-figure study to determine growth speeds for melt figures at two pressurization rates (104.4 MPa/s and 67.5 MPa/ s, see Fig. 9), for an ambient temperature of −10 °C. Then, from the plot of melt-figure growth speed vs pressurization rate (Fig. 10) we use the linear fit to the data to obtain the change in length of a melt figure associated with a change in pressure (i.e. slope of the linear fit in Fig. 10), that gives a value of 0.0472 mm/MPa. From this we can obtain an estimate for the growth of a melt figure corresponding with our estimated actual pressure spike of 36.0 MPa from the ice crushing tests.
Fig. 10. Melt figure growth rate versus pressurization rate. The two non-zero data points correspond to the slopes of the two fitted lines in Fig. 9. 6
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effects of ice shapes with respect to the shapes of hard zones that develop during crushing. It is now appropriate to make a final clarification. Allowing that the features are melt figures, we can say that they represent true adiabatic pressure melting where, due to the short durations of the pressure spikes (roughly 1 ms), the heat for the melt comes very locally from within the superheated ice itself due to its limited thermal conductivity. The melt figures form quickly (on the ascending parts of the pressure spikes) and then the associated melt refreezes quickly (on the descending portions of the pressure spikes) without contributing any melt to the liquid content of the slurry layer. That is, there is no net timeaveraged heat flow from or to the ice in the paths of the melt figures. As stated previously the source of the liquid that comprises roughly 20% of the slurry is the viscous flow of the pressurized slurry (as per squeezefilm calculations (Gagnon, 1994a)) that generates the heat for some melting at the hard-zone ice surface that the slurry is in direct contact with, and some melting of ice particles already entrained in the slurry. The melt figures main role then, is with respect to the conjectured erosive process put forward earlier that relates to ice particles detaching from the hard-zone surface and entering the slurry.
phase transition from ice Ih to ice III. This is not possible, however, because the required pressure for the transition is approximately 300 MPa (Gagnon et al., 1990), implying in the case of Kim et al. (2012) an indentor load that is roughly two orders of magnitude greater than what was measured. Such high pressures have never been reported for non-ballistic ice impact and indentation experiments where maximal values are typically in the 20–70 MPa range. We finally note that the existence and characteristics of the slurry layer (including the present proposed shallow-depth Tyndall melt figures) are based entirely on in situ observations from various experiments and associated calculations. Supplementary data to this article can be found online at https:// doi.org/10.1016/j.coldregions.2019.102867.
3. Conclusions
References
High-speed imaging records from ice-crushing tests were analyzed to study the size and growth characteristics of small features that were observed at the ice/crushing-platen interface during spallation-induced pressure spikes. The visual data suggest that the features were actually small melt figures that nucleated at the ice/platen interface and propagated laterally within a shallow depth in the ice. This conclusion was partially drawn from the similarities of the small features with melt figures produced in an earlier study where ice was adiabatically pressurized in an oil-filled pressure vessel. Further supporting evidence comes from a determination of the melt-figure growth length (1.7 mm) that would have occurred, based on growth-rate versus pressurizationrate data from the earlier melt-figure study, for a typical spallationinduced pressure spike (36.0 MPa) in the ice-crushing tests. When this melt-figure growth determination is compared with the typical growth length of the features observed in the crushing tests (1.5 mm), a compelling level of agreement is indicated. The general alignment of the features with the diagonal lines of maximal confining stress in the ice sample, and the case of a twin pair of features exhibiting an angular separation similar to a crystal symmetry angle, provide further evidence that they are melt figures. The presence of tiny melt figures at the ice/platen interface during ice crushing might explain how ice particles can erode from the contacting ice surface due to the tenuous matrix of surface-weakening shallow-depth (~0.2 mm) melt figures at the ice interface during adiabatic pressure spikes. This could facilitate a unique erosive effect that occurs as the material in the top portion of this weakened layer is sheared off by, and entrained in, the ambient viscous flow of slurry. Apart from the mechanisms described above, one might wonder if crushing ice at temperatures as low as −40 °C, such as was done in the ice indentation tests conducted by Kim et al. (2012), would lead to a
Barrette, P.D., 2001. Triaxial Testing of Ice: A Survey of Previous Investigations. POAC'01. vol. 3. pp. 1375–1384. Baumann, K., Bilgram, J.H., Känzig, W., 1984. Superheated ice. Z. Phys. B Condens. Matter. 56, 315–325 (1984). Boehler, R., Guthrie, M., Molaison, J., Dos Santos, A.M., Sinogeikin, S.V., Machida, S., Pradhan, N., Tulk, C.A., 2013. Large-volume diamond cells for neutron diffraction above 90 GPa. High Pressure Res. 33 (3), 546–554. Gagnon, R.E., 1994a. Melt layer thickness measurements during crushing experiments on freshwater ice. J. Glaciol. 40 (134), 119–124. Gagnon, R.E., 1994b. Generation of melt during crushing experiments on freshwater ice. Cold Reg. Sci. Technol. 22 (4), 385–398. Gagnon, R.E., 1998. Analysis of visual data from medium scale indentation experiments at Hobson's choice ice island. Cold Reg. Sci. Technol. 28, 45–58. Gagnon, R.E., 2008. High-speed imaging of mechanisms responsible for sawtooth cyclic loading during ice crushing. In: Proceedings of IAHR 2008, Vancouver, Canada. vol. 2. pp. 983–991. Gagnon, R.E., 2013. High-speed imaging of ice-on-ice crushing. In: Proceedings of POAC 2013, Espoo, Finland. Gagnon, R.E., 2016. New friction mechanisms revealed by ice crushing-friction tests on high-roughness surfaces. Cold Reg. Sci. Technol. 131 (2016), 1–9. Gagnon, R.E., Kiefte, H., Clouter, M.J., Whalley, E., 1990. Acoustic velocities and densities of polycrystalline ice Ih, II, III, V, and VI by Brillouin spectroscopy. J. Chem. Phys. 92 (3) 1 February 1990. Gagnon, R.E., Tulk, C., Kiefte, H., 1994. Internal melt figures in ice by rapid adiabatic compression. J. Glaciol. 40 (134), 132–134. Hobbs, P.V., 1974. Ice Physics. Oxford University Press. Kaiser, G., Magun, S., 1964. Melting processes in ice crystals under increased pressure. Druck. Z. Kristallogr. 120 (6), 450–465. Kim, E., Golding, N., Schulson, E.M., Løset, S., Renshaw, C.E., 2012. Mechanisms governing failure of ice beneath a spherically-shaped indenter. Cold Reg. Sci. Technol. 78 (2012), 46–63. Kirby, S.H., Durham, W.B., Heard, H.C., 1985. Rheologies of H2O ices Ih, II and III at high pressures: a progress report. In: Klinger, J., Benest, D., Dollfus, A., Smoluchowski, R. (Eds.), Ices in the Solar System. D. Reidel Publ. Comp, Hingham, MA, pp. 89–107. Lee, G.W., Evans, W.J., Yoo, C., 2007. Dynamic pressure-induced dendritic and shock crystal growth of ice VI. PNAS 104 (22), 9178–9181 May 29, 2007. Spencer, P.A., Masterson, D.M., 1993. A geometrical model for pressure aspect-ratio effects in ice-structure interaction. In: Proceedings of the 12th International Conference on Offshore mechanics and Arctic Engineering, OMAE 1993. 4. pp. 113–117.
Acknowledgements R.E. Gagnon would like to thank OCRE/NRC for its support of this research. He is also grateful to Austin Bugden for technical assistance during the ice-crushing test program. C.A. Tulk acknowledges support from the DOE Office of Science User Facilities.
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Cold Regions Science and Technology journal homepage: www.elsevier.com/locate/coldregions
Evidence for Tyndall melt-figure production during spallation-induced pressure spikes associated with ice crushing
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R.E. Gagnona, , C.A. Tulkb a b
Ocean, Coastal and River Engineering, National Research Council Canada, St. John's, NL, Canada Neutron Sciences Directorate, Oak Ridge National Laboratory, Oak Ridge, TN, USA
A R T I C LE I N FO
A B S T R A C T
Keywords: Ice crushing Melt figures Ice/melt slurry layer Pressure spikes Hard-zone erosion
In discussing ice crushing in the brittle regime Gagnon (2016) had speculated that small Tyndall melt figures, functioning in conjunction with a previously observed thin squeeze-film slurry layer of melt and ice particles at the ice/structure interface, could play a role in the removal of ice from the interface. Here we present supporting evidence for the existence of the melt figures. Using high-speed imaging, small features were observed to rapidly appear and grow in size at the ice/surface interface during pressure spikes caused by spallation of ice in the contact zone during crushing experiments conducted at −10 °C. The observations correlate with data from a previous study of inwardly-propagating Tyndall melt figures that nucleate at the surface of ice, situated in an oilfilled pressure vessel, when subjected to rapid adiabatic pressure increments. That is, during the ice-crushing experiments the mean growth length of the features was 1.5 ± 0.6 mm, where associated ice/surface interfacial pressure spikes (from similar tests) were about 36 MPa. For comparison, the earlier melt-figure study yielded a growth length of ~ 1.7 mm, which is within reasonable agreement with the ice-crushing value for the same rapid pressure increment. Furthermore, the features had orientations that generally were aligned with the two diagonal axes that connected opposing corners of the four-sided pyramid-shaped samples, where confinement was greatest. Hence the internal stress, and associated superheating, in hard-zone ice at the crushing interface during pressure spikes was greatest along the two axes. The features tended to grow in these directions, where the most heat was available, so this suggests they were melt figures. An incidence where a twin pair of features exhibited an angular separation close to a crystal symmetry angle also suggests the features were melt figures. The orientation data generally indicate that orientations of melt figures in non-uniformly rapidly-stressed ice may differ from orientations in uniformly stressed ice. We conjecture that in the present study small melt figures form a tenuous liquid matrix of shallow depth (roughly 0.2 mm) in the hard-zone ice surface during pressure spikes. A unique erosive effect may occur as the material in the top portion of this weakened layer is sheared off by, and entrained in, the ambient viscous flow of slurry.
1. Ice crushing characteristics Various aspects of ice crushing in the brittle regime, noted by Gagnon (2016), are illustrated in Fig. 1. The drawing at the left shows an ice shape crushing against a flat platen at a nominal constant rate. In the central region of the contact zone we note a hard zone, where the ice is relatively intact, that causes high interface pressure (~20–70 MPa) at the platen-ice contact region. At the sides of the hard zone is softer crushed ice that essentially is shattered spall debris from prior spalling events. The interface pressure is relatively low (~0–10 MPa) where the crushed ice contacts the platen. At the interface between the hard-zone ice and the platen one can see the thin slurry layer. Note that the slurry is partially liquid and when the slurry layer ⁎
flows out of the hard-zone region it tends to contribute to the wetness of the surrounding crushed ice in the soft zone. Also note that the soft zone itself generates some liquid, due to the same crushing processes, at iceice contact between ice fragments during the extrusion and flow of the crushed ice away from the high-pressure zones (Gagnon, 2013). At the right of the figure we have a schematic showing a spalling fracture just prior to the spall shattering and converting to crushed ice. Here we note that when such a spall forms and shatters there will be a consequent drop in global load and a subsequent increase in stress on the remaining hard-zone ice that causes a sharp spike in interface pressure. Elastic energy in the ice/apparatus system rapidly reduces when the ice and platen surge towards one another as ice is removed from the hard zone due to the flow of the squeeze-film slurry layer during the load drop.
Corresponding author. E-mail address: [email protected] (R.E. Gagnon).
https://doi.org/10.1016/j.coldregions.2019.102867 Received 10 December 2018; Received in revised form 2 May 2019; Accepted 15 August 2019 Available online 16 August 2019 0165-232X/ Crown Copyright © 2019 Published by Elsevier B.V. All rights reserved.
Cold Regions Science and Technology 167 (2019) 102867
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Fig. 1. Schematics showing the essential characteristics of ice crushing against a flat rigid surface. The scenario depicted in the right schematic occurs after the scenario depicted at the left (more details are given below). To highlight the hard zone only a portion of the ice contact zone is shown, that is, the crushed ice at the sides extends farther than what is shown.
2. Experimental and analytical results
Even though the ice may be moving at a nominal constant rate during a crushing test there will nevertheless be compliances associated with the ice, platen and drive system so that the actual relative movement of the ice and platen towards each other is intermittent (Gagnon, 1994a). The removal of ice from the hard-zone surface cannot be fully explained by the melting that occurs due to heat generated by the viscous flow of the slurry since only roughly 20% of the slurry is melt (Gagnon, 1994b).
Fig. 2 shows data from a crushing test on a large single-crystal ice sample (Gagnon, 1994a), where the c-axis was in the loading direction and the test temperature was −10 °C. The mono-crystalline sample ensured good visibility, through the ice specimen, of details of the ice crushing behaviour at the ice-platen contact interface since there were no obscuring intergranular cracks. In this case there are pressure data from a small pressure transducer that was located at the ice-platen interface at the approximate hard-zone location. Furthermore, the figure
Fig. 2. Sections of the load, pressure and liquid-sensor data from a crushing test on a large single-crystal ice sample. From Gagnon, 1994a. 2
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shows data from a small (resistance-type) liquid sensor that was located on the face of the pressure transducer. The course phase relationships of data in Fig. 2 have been discussed before (Gagnon, 1994a). Fig. 2 indicates that the associated peaks in load, pressure and liquid thickness occur at roughly the same time. Closer inspection of seven of the prominent load-drop events revealed that the pressure-spike peak typically occurred at ~0.8 ± 0.2 ms after the load peak, and the peak in liquid thickness occurred at ~1.2 ± 0.2 ms after the load peak. Hence, the sequence involves first the spall formation (i.e. initiation of the sharp drop in global load); followed by the increase in stress on the remaining ice (i.e. the pressure spike); followed by the spike in liquid thickness that occurs at the time corresponding to roughly the midpoint of the drop in load (~1.4 ± 0.1 ms after the load peak), where the ice and platen are moving the fastest towards one another and squeezing the viscous slurry out of the contact zone at the fastest rate, thereby creating melt at the fastest rate. The sequence of events, including calculations of the amount of melting and the layer thickness, are discussed by Gagnon (1994a, 2016). Note that the calculations (Gagnon, 1994a) are based on squeeze-film theory that explains why the layer is thinner on the ascending portions of the load peak and at the bottom of the load drop, where the relative speed of the ice moving towards the platen is low. At the midpoint of the load drop the relative speed is much higher and the theory consequently indicates a thicker layer, as is consistent with Fig. 2. The calculations were based on the nominal displacement of the test actuator, the measured load and known compliances of the ice/apparatus system, and the measured hard-zone contact areas. Here we briefly describe what melt figures (a.k.a. negative crystals, in the context of mineralogy) are. If ice near its melting temperature is rapidly pressurized, such as inside a fluid-filled pressure vessel, its melting temperature rapidly decreases, as stipulated by the well-known Clausius-Clapeyron equation (Hobbs, 1974; Baumann et al., 1984). This puts the bulk ice into a superheated state so that the excess heat causes the growth of liquid-filled, sometimes faceted, structures inside the ice. Gagnon et al. (1994) described dendritic fern-like melt figures that nucleated at the ice surface of mono-crystalline samples and grew inwards at a rate proportional to the rate of pressure application (Fig. 3, and the included AVI file ‘Melt_Figure_Growth.avi’). Relieving the pressure reversed the growth process and caused the figures to shrink at a rate proportional to the rate of decompression. Advancing dendrites were very thin (~20 μm). In contrast to the dendritic figures, diskshaped, liquid-filled compression melt fractures were also created by the adiabatic pressurization. These nucleated within the crystal matrix when a certain degree of superheating had been reached. Pressure vessels have been used extensively to study ice mechanics in the context of ice engineering and glaciology, as illustrated in the survey by Barrette (2001). Fundamental studies of nucleation and growth of ice crystals and melt figures, and structural and acoustic properties of high-pressure ice polymorphs, have also been conducted using pressure vessels (e.g. Kaiser and Magun, 1964; Baumann et al., 1984; Gagnon et al., 1990; Kirby et al., 1985), including diamond anvil cells (e.g. Lee et al., 2007; Boehler et al., 2013). Note that other than the study of Gagnon et al. (1994), no other data are available on melt-figure growth rate as a function of pressurization rate. During recent re-analysis of high-speed imaging (30,000 images/s) records from ice crushing experiments (Gagnon, 2008), it was observed that small faint features appeared at the hard zone/platen interface that had characteristics reminiscent of the melt figures observed by Gagnon et al. (1994). The ice samples were large single-crystals where the c-axis was in the loading direction. The ice crushing experiments were set up for relatively large-scale viewing of the ice-crushing behavior where the field of view of the ice/platen interface was around 43 mm, whereas the field of view for the melt-figure study was about 2.2 mm. Additionally, the lighting was different in the two cases, i.e. the lighting was optimized for observing melt figures in the earlier study and not so for the ice crushing study. Nevertheless, it was possible to identify and catalog
Fig. 3. Growth of a dendritic melt figure parallel to the ice crystal basal plane as pressure was elevated during one stroke of the hand pump. The increment in time between consecutive images was 1/15 s. The pressurization rate was 623 bars/s. The diameter of the circular aperture is ~2.2 mm. The ambient temperature was −5 °C. From Gagnon et al., 1994.
several (21) small faint elongated features that appeared within the hard-zone surface interface during pressure spikes. Fig. 4 shows some examples. Common characteristics of the features were: (1) They occurred during pressure spikes associated with spalling events; (2) They rapidly appeared (within one image interval) on the increasing side of the pressure spike and retracted during the latter part of the spike. For example, Fig. 5 (and the included AVI file ‘Faint_Object_Growth_and_Retraction.avi’) shows images illustrating the growth and retraction of a feature. (3) A significant observation (discussed later) is that there were two fairly distinct orientations that the features had in the plane of view. Of the nineteen features that were suitable to use for angular measurements, thirteen of the them leaned towards the right at an angle of 44 ± 13° from the vertical axis and six of the features leaned towards the left at an angle of 47 ± 17°, that is, the angular separation between the two groups was 91 ± 21°. (4) It seemed that they grew in the direction where the most excess heat was 3
Cold Regions Science and Technology 167 (2019) 102867
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Fig. 4. Some examples of the small features (inside the outlined areas) from an ice crushing experiment (Gagnon, 2008) that had characteristics similar to melt figures observed by Gagnon et al. (1994). The images are enhanced to make the small features more visible. The variable-shaped dark areas of the images correspond to relatively-intact hard-zone ice, where the interface contact pressure with the transparent crushing platen is high. The white areas encompassing the dark regions generally correspond to low interface-pressure soft-zone crushed ice. The width of each image box is ~12.6 mm.
available from the pressure-induced super-heating effect. For example, they grew away from any nearby spalling event. (5) They grew mainly laterally within a thin layer of ice at the surface of the hard-zone interface. This common characteristic is explained in the following paragraph. The evidence that the faint features grew laterally within a thin top layer of the hard zones is as follows: 1. The confining geometry of the sloped sides of the bulk ice shape and the even gentler sloped sides of the intact-ice process surface throughout the crushing event implied that the pressure, and degree of ice compression and superheating, was maximal at the interface and dropped off significantly with depth away from the interface. By definition, melt figures grow into regions where the most excess heat, from pressure-induced superheating, is available for melting. That implies that if the faint features were in fact melt figures then they would tend to grow in directions close to the interface, i.e. laterally within a thin top ice layer. 2. If there was a tendency for the faint features to grow in non-lateral directions, for example in directions closer to the normal to the interface, then the distribution of maximal feature lengths (from the perspective of the camera viewing in the normal direction) shown in Fig. 6 would be significantly populated throughout the range from 0 mm to the higher values. However, the data in the figure indicates an average length value of 1.5 mm with a relatively tight standard deviation of ± 0.6 mm, that is, very few data points are less than 1 mm, implying that the faint features do indeed grow in directions close to the interface. In consideration of point 1 above, this suggests that they were melt figures. 3. From the analysis below, for a typical pressure spike of 36.0 MPa there is good agreement between the average apparent maximal length of the faint features in the crushing tests (1.5 ± 0.6 mm) and the growth length of melt figures from the earlier study (1.7 mm). And we know from point 2 above that the growth of the faint features is only in lateral directions. These two facts are mutually consistent if we allow that the faint features are melt figures.
Fig. 5. A numbered set of sequential images of a typical small faint feature (inside the circle) from an ice crushing experiment (Gagnon, 2008). The growth and retraction characteristics of the feature are similar to those of melt figures observed by Gagnon et al. (1994). The images were captured at 30,000 images/ s and are enhanced to make the small feature more visible. The dark area of the images corresponds to relatively-intact hard-zone ice, where the interface contact pressure with the transparent crushing platen is high. The white area encompassing the dark region corresponds to low interface-pressure soft-zone crushed ice. The width of each image box is ~12.6 mm.
Fig. 6. Maximal feature length versus measurement number for the 21 small faint features that were cataloged from the ice crushing experiment. Measurement numbers are indexes that started at a certain time in the visual record, with the first measurement, and progressed forward in time through the record to the last measurement. The ice-crushing experiment was reported by Gagnon (2008). The test was run at −10 °C with a nominal actuator speed of 3.2 cm/s. Length measurements, obtained from the high-speed images, were accurate to within 1 pixel (~0.2 mm). 4
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Our intention in this study is to demonstrate that the features observed during the crushing experiments have the same characteristics as melt figures observed during rapid adiabatic pressurization of ice. One means of providing convincing evidence for this will rely on having a good estimate for the actual pressure-spike value associated with a typical spalling event, that is, where the hard zone size and shape, and the spall characteristics, with respect to the pressure-sensor particulars have been reasonably accounted for. We now describe the strategy used to estimate what the actual value of pressure spikes are during spalling events. To do this we first note that the highest non-spike pressure recorded was approximately 60 MPa, as seen in a few tests using the same apparatus and ice type. Since the hard zones were typically a few square centimeters in area, it is reasonable to assume that this maximal nonspike pressure corresponds to those occasional instances where the shape, location and size of the hard zone caused it to fully encompass the circular end of the cylindrical pressure sensor that has a surface area of 0.5 cm2. This implies that for a typical pressure sawtooth we can estimate the fractional areal coverage of the pressure sensor by hardzone ice by taking the measured pressure on the sensor at the base of the pressure spike and assuming that a portion of the surface area of the sensor is covered by hard-zone ice (where the pressure is 60 MPa) and the remainder is covered by soft-zone ice (where the pressure is 5 MPa). This yields a unique value for the fractional hard-zone coverage. For any given pressure range, if we choose the largest pressure spikes in that pressure region we will have some assurance that the hard-zone area under the sensor is not encompassed to any significant extent by the spall that forms. Furthermore, we must choose a particular type of pressure spike, that is, spikes where the pressure just prior to the spike is similar to the value that it is just after the spike, implying that the spallation that caused the spike most likely occurred outside of the area of the pressure sensor. Hence, by choosing the spikes with the highest magnitude (6.5–18.5 MPa) that fit the latter criteria we achieve the greatest likelihood of obtaining a good actual spike-height estimate. In other words, for the chosen pressure spikes the amounts of hard-zone ice contact and soft-zone ice contact under the pressure sensor face have not changed during the ascending portion of the pressure spike, during which no relative movement of the ice and sensor towards each other occurs. Recall that the rapid surge of the ice and crushing platen towards one another starts during the descending part of the pressure spike and is greatest at the midpoint of the drop in load. Note that the crushed-ice soft zone does not contribute anything to the pressure spikes. Generally there are many instances in the lowerpressure data from the pressure sensor, where low pressure indicates that only soft-zone ice is in contact with the sensor. In those cases no spike is registered by the sensor when a spallation occurs.
Fig. 8. Data acquired by analyzing a set of pressure spikes from the same ice crushing experiment corresponding to Fig. 7. The data points (red squares) with fractional coverage greater than 0.25 demonstrate consistency, and therefore yield a reasonable estimate for a typical pressure spike height (36.0 ± 2.4 MPa). The data points (blue diamonds) with fractional coverage less than 0.25 lack consistency, for reasons discussed in the text, and consequently cannot be used to estimate a typical pressure spike height. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
As an example of the strategy, consider the suitably-chosen spike shown in Fig. 7 where we note that the pressure just before the spike is about 33.3 MPa, which implies a coverage of 52% from the hard-zone coverage estimate. Hence, the magnitude of the measured pressure spike (18.5 MPa) is actually only 52% of the true pressure spike on the hard-zone ice since only 52% of the sensor is covered by the hard-zone ice. Therefore we can estimate a true value for a typical pressure spike by multiplying the value of the measured spike by 1/0.52, to yield 35.6 MPa. This would be the measured pressure spike magnitude if the sensor had been fully encompassed by the hard zone and if the spallation occurred outside the pressure sensor area. We have performed this type of analysis for several suitably-chosen pressure spikes in the load record and plotted the estimated actual pressure-spike height in each case in Fig. 8. We note that for data points associated with fractional coverages higher than 0.25 that there is good consistency, where the mean value and standard deviation for these data are 36.0 ± 2.4 MPa. The likely reason why the data points at the left of the plot in Fig. 8, for fractional area coverages less than 0.25, lead to overestimates of spike values (that should not be used) is that at the lower sensor loads the assumption that the sensor is fully covered by only soft ice, or portions of soft ice and hard ice, is probably false. That is, at low
Fig. 7. Graph illustrating the strategy used to analyze pressure spikes. This particular ice crushing experiment was reported by Gagnon (1994b). The test was conducted at −10 °C with a nominal actuator speed of 1.5 cm/s. 5
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This pressure spike would cause a melt figure to grow to a length of 1.7 mm, which agrees quite well with the average length of the features observed in the ice crushing study (1.5 mm), considering the radically different nature of the two studies. The data shown in Figs. 9 and 10 essentially indicate that at these adiabatic pressurization rates (~104 MPa/s and ~68 MPa/s) the rate does not play a role in the growth length of the figures, rather it is the magnitude of the pressure increment that determines the melt-figure growth length (i.e. 0.0472 mm/MPa). We have assumed that this applies even when pressurization rates are as high as those associated with the pressure spikes in the crushing tests (~ 37 GPa/s). The agreement of the melt-figure lengths from the pressure vessel tests and the feature lengths, if we allow that they are melt figures, from the crushing test is consistent with this assumption. We now draw the reader's attention back to the important earlier observation that the features generally had two typical orientations (with some degree of variability) in the plane of view, where the angular separation between the orientations was 91 ± 21°. In a single incidence a twin pair of the features started growth at the same time and from the same location (see the image at the lower right of Fig. 4), where the angular separation between them (~ 116°) was quite close to the crystal symmetry angle of 120°. Gagnon et al. (1994) observed meltfigure growth in the basal plane with orientations that reflected the crystal symmetries (0°, 60°, 120°) and also melt figures with two orientations in a plane perpendicular to the basal plane where the angular separation was 90°. The similarity of the latter with the general angular separations we observed for the features, and the similarity of the angle between the twin pair of features with the symmetry angle of 120°, suggested a connection with the crystal structure though it was not clear why the feature orientations didn't generally reflect the basal plane symmetries (i.e. 0°, 60°, 120°). We offer that these observations may be understood by considering the different ice stress regimes in the two cases. The pressure vessel experiments of Gagnon et al. (1994) involved subjecting the small mono-crystalline ice samples to a uniform hydrostatic stress whereas here we are discussing relatively large monocrystalline pyramid-shaped ice samples that are loaded uniaxially from the top of the pyramid, thereby creating a non-uniform stress field in the ice sample. Allowing that the features are melt figures, the implication is that non-uniform stress fields in ice can alter/perturb the orientations that adiabatic pressure-induced melt figures would normally have in uniformly-stressed ice where the crystalline structure (that reflects variations in the molecular energy levels in the lattice) is the determining factor for melt-figure growth directions. In that connection recall that the two typical orientations of the features (i.e. 44 ± 13° to the right of the vertical axis and to the left of the axis at 47 ± 17°) closely aligned with the diagonals connecting opposing corners of the four-sided pyramid-shaped ice sample. Hence, during loading of the sample confinement was greatest at the corners, implying that internal stress and associated superheating in hard-zone ice at the crushing interface during pressure spikes was greatest along the diagonals. This implies that the features were melt figures, since they tended to grow in directions where the most heat was available. The twin pair of features (Fig. 4, lower right), mentioned above, may have been a special case. Allowing that they are melt figures, we suggest that since the twin pair originated simultaneously from the same location their angular separation (that falls within the general angular variability of singular features) was more inclined to reflect the actual crystal symmetry, as observed. This also provides evidence that the features were melt figures. The influence that ice sample shape has on confinement aspects of the bulk ice is manifested in the typical shapes of hard zones that consequently develop during crushing. For example, Gagnon (1998) observed X-shaped hard zones during crushing tests on large four-sided truncated pyramid-shaped ice features. The ‘arms’ of the ‘X’ aligned with the corners of the pyramids, where confinement was greatest. Spencer and Masterson (1993) have discussed aspect-ratio
Fig. 9. Melt figure growth length versus time for two melt figures. The growth rates (i.e. the slopes of the fitted lines) are different because the pressurization rates were different.
pressures (i.e. small sensor-face loads) a portion of the sensor face may not be in contact with any ice, whether soft or hard. Our assumption would then lead us to overestimate the soft-zone coverage and thereby underestimate the hard-zone ice coverage. This, in turn, would lead us to overcompensate for the assumed small size of the hard-zone coverage on the sensor face when calculating the actual hard-zone pressure. The trend-slope of the first four points at the left of Fig. 8 supports this assertion since the error, caused by no ice contact on a portion of the sensor face, becomes more likely as the load on its face (i.e. the average pressure) gets smaller. From these considerations we may determine the growth length of a melt figure from the study of melt figures (Gagnon et al., 1994) that corresponds with a typical pressure spike (36.0 MPa) from the icecrushing study of Gagnon (1994b). To do this we first use video and pressure records from the melt-figure study to determine growth speeds for melt figures at two pressurization rates (104.4 MPa/s and 67.5 MPa/ s, see Fig. 9), for an ambient temperature of −10 °C. Then, from the plot of melt-figure growth speed vs pressurization rate (Fig. 10) we use the linear fit to the data to obtain the change in length of a melt figure associated with a change in pressure (i.e. slope of the linear fit in Fig. 10), that gives a value of 0.0472 mm/MPa. From this we can obtain an estimate for the growth of a melt figure corresponding with our estimated actual pressure spike of 36.0 MPa from the ice crushing tests.
Fig. 10. Melt figure growth rate versus pressurization rate. The two non-zero data points correspond to the slopes of the two fitted lines in Fig. 9. 6
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effects of ice shapes with respect to the shapes of hard zones that develop during crushing. It is now appropriate to make a final clarification. Allowing that the features are melt figures, we can say that they represent true adiabatic pressure melting where, due to the short durations of the pressure spikes (roughly 1 ms), the heat for the melt comes very locally from within the superheated ice itself due to its limited thermal conductivity. The melt figures form quickly (on the ascending parts of the pressure spikes) and then the associated melt refreezes quickly (on the descending portions of the pressure spikes) without contributing any melt to the liquid content of the slurry layer. That is, there is no net timeaveraged heat flow from or to the ice in the paths of the melt figures. As stated previously the source of the liquid that comprises roughly 20% of the slurry is the viscous flow of the pressurized slurry (as per squeezefilm calculations (Gagnon, 1994a)) that generates the heat for some melting at the hard-zone ice surface that the slurry is in direct contact with, and some melting of ice particles already entrained in the slurry. The melt figures main role then, is with respect to the conjectured erosive process put forward earlier that relates to ice particles detaching from the hard-zone surface and entering the slurry.
phase transition from ice Ih to ice III. This is not possible, however, because the required pressure for the transition is approximately 300 MPa (Gagnon et al., 1990), implying in the case of Kim et al. (2012) an indentor load that is roughly two orders of magnitude greater than what was measured. Such high pressures have never been reported for non-ballistic ice impact and indentation experiments where maximal values are typically in the 20–70 MPa range. We finally note that the existence and characteristics of the slurry layer (including the present proposed shallow-depth Tyndall melt figures) are based entirely on in situ observations from various experiments and associated calculations. Supplementary data to this article can be found online at https:// doi.org/10.1016/j.coldregions.2019.102867.
3. Conclusions
References
High-speed imaging records from ice-crushing tests were analyzed to study the size and growth characteristics of small features that were observed at the ice/crushing-platen interface during spallation-induced pressure spikes. The visual data suggest that the features were actually small melt figures that nucleated at the ice/platen interface and propagated laterally within a shallow depth in the ice. This conclusion was partially drawn from the similarities of the small features with melt figures produced in an earlier study where ice was adiabatically pressurized in an oil-filled pressure vessel. Further supporting evidence comes from a determination of the melt-figure growth length (1.7 mm) that would have occurred, based on growth-rate versus pressurizationrate data from the earlier melt-figure study, for a typical spallationinduced pressure spike (36.0 MPa) in the ice-crushing tests. When this melt-figure growth determination is compared with the typical growth length of the features observed in the crushing tests (1.5 mm), a compelling level of agreement is indicated. The general alignment of the features with the diagonal lines of maximal confining stress in the ice sample, and the case of a twin pair of features exhibiting an angular separation similar to a crystal symmetry angle, provide further evidence that they are melt figures. The presence of tiny melt figures at the ice/platen interface during ice crushing might explain how ice particles can erode from the contacting ice surface due to the tenuous matrix of surface-weakening shallow-depth (~0.2 mm) melt figures at the ice interface during adiabatic pressure spikes. This could facilitate a unique erosive effect that occurs as the material in the top portion of this weakened layer is sheared off by, and entrained in, the ambient viscous flow of slurry. Apart from the mechanisms described above, one might wonder if crushing ice at temperatures as low as −40 °C, such as was done in the ice indentation tests conducted by Kim et al. (2012), would lead to a
Barrette, P.D., 2001. Triaxial Testing of Ice: A Survey of Previous Investigations. POAC'01. vol. 3. pp. 1375–1384. Baumann, K., Bilgram, J.H., Känzig, W., 1984. Superheated ice. Z. Phys. B Condens. Matter. 56, 315–325 (1984). Boehler, R., Guthrie, M., Molaison, J., Dos Santos, A.M., Sinogeikin, S.V., Machida, S., Pradhan, N., Tulk, C.A., 2013. Large-volume diamond cells for neutron diffraction above 90 GPa. High Pressure Res. 33 (3), 546–554. Gagnon, R.E., 1994a. Melt layer thickness measurements during crushing experiments on freshwater ice. J. Glaciol. 40 (134), 119–124. Gagnon, R.E., 1994b. Generation of melt during crushing experiments on freshwater ice. Cold Reg. Sci. Technol. 22 (4), 385–398. Gagnon, R.E., 1998. Analysis of visual data from medium scale indentation experiments at Hobson's choice ice island. Cold Reg. Sci. Technol. 28, 45–58. Gagnon, R.E., 2008. High-speed imaging of mechanisms responsible for sawtooth cyclic loading during ice crushing. In: Proceedings of IAHR 2008, Vancouver, Canada. vol. 2. pp. 983–991. Gagnon, R.E., 2013. High-speed imaging of ice-on-ice crushing. In: Proceedings of POAC 2013, Espoo, Finland. Gagnon, R.E., 2016. New friction mechanisms revealed by ice crushing-friction tests on high-roughness surfaces. Cold Reg. Sci. Technol. 131 (2016), 1–9. Gagnon, R.E., Kiefte, H., Clouter, M.J., Whalley, E., 1990. Acoustic velocities and densities of polycrystalline ice Ih, II, III, V, and VI by Brillouin spectroscopy. J. Chem. Phys. 92 (3) 1 February 1990. Gagnon, R.E., Tulk, C., Kiefte, H., 1994. Internal melt figures in ice by rapid adiabatic compression. J. Glaciol. 40 (134), 132–134. Hobbs, P.V., 1974. Ice Physics. Oxford University Press. Kaiser, G., Magun, S., 1964. Melting processes in ice crystals under increased pressure. Druck. Z. Kristallogr. 120 (6), 450–465. Kim, E., Golding, N., Schulson, E.M., Løset, S., Renshaw, C.E., 2012. Mechanisms governing failure of ice beneath a spherically-shaped indenter. Cold Reg. Sci. Technol. 78 (2012), 46–63. Kirby, S.H., Durham, W.B., Heard, H.C., 1985. Rheologies of H2O ices Ih, II and III at high pressures: a progress report. In: Klinger, J., Benest, D., Dollfus, A., Smoluchowski, R. (Eds.), Ices in the Solar System. D. Reidel Publ. Comp, Hingham, MA, pp. 89–107. Lee, G.W., Evans, W.J., Yoo, C., 2007. Dynamic pressure-induced dendritic and shock crystal growth of ice VI. PNAS 104 (22), 9178–9181 May 29, 2007. Spencer, P.A., Masterson, D.M., 1993. A geometrical model for pressure aspect-ratio effects in ice-structure interaction. In: Proceedings of the 12th International Conference on Offshore mechanics and Arctic Engineering, OMAE 1993. 4. pp. 113–117.
Acknowledgements R.E. Gagnon would like to thank OCRE/NRC for its support of this research. He is also grateful to Austin Bugden for technical assistance during the ice-crushing test program. C.A. Tulk acknowledges support from the DOE Office of Science User Facilities.
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